Applied Statistics • Chapter 2: Analysis of univariate data • Representations and graphs. • Frequency tables. • Bar charts, pictograms, histograms, frequency polygons and box plots • Numerical summary. • Measures of location. • Measures of spread. • Measures of form. • Recommended reading: • Bad charts • Capítulos 3 a 7 del libro de Portilla (2004)
Applied Statistics 2.1: Representations and graphs • DESCRIPTION OF QUALITATIVE VARIABLES • Absolute frequency • Relative frequency • Bar chart • Pie chart • DESCRIPTION OF QUANTITATIVE VARIABLES • Absolute frequency / cumulative absolute frequency • Relative frequency / cumulative relative frequency • Histogram • Frequency polygon Recommended reading: • Capítulos 3 y 4 del libro de Portilla (2004)
Applied Statistics Description of qualitative variables SAMPLE: 70 madrileño university students VARIABLE: Preferred political party OBJECTIVE: Classification and representation of the information PP IU Otros PP PSOE Otros Otros IU PP IU PSOE PSOE UPD IU PP PSOE IU PP PSOE Otros PSOE IU IU PSOE IU IU PSOE PSOE PP PSOE PP PP PSOE IU UPD PP PSOE UPD PSOE PP Otros IU IU PSOE IU PP PSOE IU PSOE IU IU PSOE UPD UPD IU PP PSOE IU PSOE IU PP PSOE IU PSOE PSOE UPD UPD PP PP PSOE
Applied Statistics The frequency table Absolute frequency Relative frequency = 15/70 = 23+15+20+7+5 = 0,33+0,21+ …+0,07
Applied Statistics The general outline of a frequency table = n1/N = n1 + n2 +… + nk = f1 + f2 +… + fk
Applied Statistics The bar chart
Applied Statistics How to lie with bar charts Data on the previous computer of iMac owners
Applied Statistics • It appears that nearly everyone buys Macs …
Applied Statistics • … but now not so much!
Applied Statistics Comparative bar charts http://cnx.org/content/m10927/latest/
Applied Statistics The pie chart 7% 10% 33% 29% 21%
Applied Statistics The pictogram PSOE PP IU UPD OTROS The area of the graph is proportional to the frequency.
Applied Statistics A real example of a pictogram
Applied Statistics How to lie with pictograms Letting height be proportional to frequency gives a false impression.
Applied Statistics • Exercise Crimes commited in Chicago between 5/11/2009 and 5/12/2009 Summarize these data in graphical form Chicago crime database
Applied Statistics • Exercise • Final grades in a statisticscourse: Is this a nominal or an ordinal variable? What percentage of the students didn’t pass? Are there any other graphs that could be useful here?
Applied Statistics • Exercise (Test question) • The 40 students in a statisticsclassratetheirlecturerfrom 1 (extremelyboring) to 5 (fantastic). Thetablepartially shows thesurveyresults. • Complete thetable.
Applied Statistics • Exercise (Test question) • The following table comes from the CIS survey of January 2011. The values are given as (approximate) percentages of a total number of 2478 respondents.: Which of the following affirmations is correct? The number of respondents who have a lot of confidence (muchaconfianza) in the Mariano Rajoy is approximately 619. Approximately 1953 of the respondents have little or no confidence (poca o ningunaconfianza) in the leader of the PP. The relative frequency of respondents who don’t know (NS) or don’t reply (NC) is 0.19. None of the above.
Applied Statistics • Exercise (Examquestion) • The following pie chart shows the distribution of the autonomous communities visited by foreign tourists. Which of the following is the correct response? The percentage of tourists who visit the islands is lower than the percentage for the rest of the destinations. The percentage of tourists who visit the islands is higher than the percentage for the rest of the destinations. Cataluña and the Comunidad de Madrid are the communities with the highest percentages of foreign tourists. None of theabove.
Applied Statistics • Exercise (Examquestion) • The following pie chart concerns the voting concerns of students at the University of Houston University before the 2010 elections. • Which of the following affirmations is correct? • 160 students said that the main issues were Jobs or Immigration. • 327 students said that the main issues were Public schools or Health care. • 25 students said that the main issue was Other. • 259 students said that the main issue was College costs.